The hiring process consists of three parts,I made it to round one and didn't get an invite to round two--
1) First thing I had to do was complete a two part online test (1st part is like a very simple IQ test, 2nd part is a personality test to probably see if you match with their 14 leadership principles). After this, you're either accepted or rejected for a first round interview.
2) First round interview--two 30 minute interviews. The personalities of the interviewers were very different, the first was very low key, the second was very high energy. Phone interviews were conducted on the same day about two hours apart. The interviews weren't really either behavioral or case-based which really threw me off-- they were very entrepreneurial, problem recognition/solving focused. Be able to talk to Amazon as a company, what you think some of it's problems are, and new product suggestions. Expect interviewers to "dive deep" and get into why you're answering questions the way you are.
As a side note-- I had other friends interview for other positions (program manager, logisitics) and their questions/focus were very different than mine. Good luck and hopefully you have a better chance than I did.